This invention relates generally to precision attitude, position, velocity, and time measurement systems using satellite navigation system measurements. More specifically, the invention relates to systems and methods for inferring the differential path length of carrier wave signals between the satellite transmitter antenna and two or more receiver antennas for a set of satellite signals to enable accurate inference of the relative geospatial coordinates of the receiver antennas.
The determination of the relative coordinates of points of a distributed physical system in a geospatial reference frame has application to a number of important problems. Attitude determination is a primary example. Early techniques for determining the attitude of a rigid body were based on the use of Earth-generated field phenomena. For example, one technique used sensors to detect the magnetic field direction of the Earth to determine magnetic compass heading of the rigid body and to sense the gravitational field direction of the Earth to determine the attitude of the rigid body with respect to the local gravitational vertical. These techniques have limited precision and accuracy because of complex local variations in the magnetic and gravitational fields of the Earth, difficulties in measuring such phenomena with high resolution, and unwanted coupling effects, such as acceleration effects on the sensors.
To determine the attitude of a rigid body in geospatial coordinates with high precision and accuracy, some techniques focus on measuring phenomena whose sources are more controllable than Earth-generated magnetic and gravitational fields. Optical techniques developed in surveying have achieved the desired levels of precision and accuracy, but are difficult to employ in many operating conditions, particularly with moving bodies. Recent techniques based on determining the transmission path lengths of code-modulated radio frequency signals transmitted from navigation satellite systems, such as the United States Global Positioning System (GPS) and the functionally-similar Global Navigation Satellite System (GLONASS) operated by Russia, have transformed surveying.
The geospatial location of each transmitting GPS satellite, or other signal source, as a function of time can usually be inferred from data contained in the transmitted signal. At the typical distances from the satellite, or other navigation signal source, to the surface of the Earth, the signal transmission paths can be considered nearly parallel for a physical body whose attitude is to be measured. The difference in the path lengths of the transmissions received at two satellite receiver antennas, separated by a baseline of known length, can be used to determine the attitude of the body in the plane defined by the satellite and the two separated receiver antennas. By using three or more satellite receiver antennas, arranged on the body so that they are not co-linear, the three-dimensional attitude in geospatial coordinates can be determined.
The measurement of the transmission path length from the satellite to a receiver antenna depends on the measured characteristics of the signal. The coded information imposed on the satellite carrier wave allows an unambiguous determination of the length of the transmission path. However, path length based on the coded information can only be measured to a relatively coarse resolution. Finer resolution requires the measurement of the carrier wave itself. For example, where the chip width of the coded information for GPS is approximately 300 meters, the wavelength of the GPS carrier signal is approximately 19 centimeters. This allows resolution of the transmission path length to fractions of a centimeter by phase measurement techniques within the GPS receiver.
Note that all carrier waves are identical and indistinguishable from each other. As a result, when the phase of the wave is determined at the receiver antenna, it is ambiguous which specific cycle of the carrier wave is being measured. The total path length from the satellite antenna to the receiver antenna is the sum of the GPS receiver""s measured fraction of a cycle and an unknown number of integer cycles. Determining the specific wave cycle of the carrier wave that is being measured in phase is called cycle ambiguity resolution (also referred to as integer ambiguity resolution).
Typically, the information coded in the transmitted signal is used to bound the range in which the possible integer carrier cycles can exist. The code measurement for an individual signal establishes the maximum and minimum transmission path lengths possible for that signal. This bounding process is performed for all the satellite signals employed in the solution. The projection of these bounds into the solution space according to the direction vectors between the receiver antenna and the transmitter antenna establishes the geometric structure of the solution space. The correct solution for the numbers of integer cycles between the transmitter and the receiver antennas is the set of answers that satisfies all the constraints within the solution space. In practice, this process is usually done with single differences of measurements between antennas when the inter-receiver clock delays are well known, and with double difference measurements between receiving antennas and between signal transmitters when the inter-antenna time delay is not well known.
Techniques have arisen to perform the steps of determining the correct number of integer carrier cycles and measuring the fractional phase within a cycle. The performance of these techniques is evaluated based on the reliability of correctly resolving the integer values and the accuracy of the resulting solution. The existing methods are suboptimum in each of these regards.
The use of carrier cycle ambiguity resolution is not limited to the determination of body attitude. Similar techniques can be used to determine the vector offsets between two or more GPS antennas that are not rigidly fixed to the same body. In one case, the first or xe2x80x9creferencexe2x80x9d receiver may be fixed at a known surveyed location, while the second GPS receiver may be on a moving body. The purpose is to correct errors in the moving GPS receiver using data calibrated in accuracy by the reference receiver. The use of carrier cycle ambiguity resolution for this mode of xe2x80x9cdifferentialxe2x80x9d GPS is often referred to as kinematic or real-time kinematic (RTK) GPS.
In another case, the first receiver may be at one unknown or moving location, and the second GPS receiver may be at a second unknown or moving location. In this case, the relative vector between the two GPS receivers is of interest. In yet another case, the use of carrier cycle ambiguity resolution can be focused on correcting the time measurement between a GPS reference receiver and a second remote GPS receiver.
In one aspect, the invention features a method for use in a positioning system having an array of satellite navigation system antennas simultaneously receiving signals emitted from a plurality of signal transmitters. The method determines an attitude of the array by determining a first set of potential solutions for a first baseline vector for any pair of antennas in the array and a second set of potential solutions for a second baseline vector for any other pair of antennas in the array. Each potential solution in the first set is compared with each potential solution in the second set to determine a degree of geometric consistency between each pair of compared solutions. One of the pairs of compared potential solutions is selected as representative of the attitude of the array if the corresponding baseline vectors satisfy predetermined criteria. One embodiment of the method simultaneously compares three sets of potential solutions for three different baseline vectors. Also, array attitude determinations can be improved by averaging the array attitude determined from multiple baseline vectors with correct solutions using angle offsets between antennas.
The sets of potential solutions can be determined for every baseline vector in the array or as baseline vectors are needed to determine the array attitude. More specifically, one embodiment of the method determines the sets of potential solutions for the baseline vectors of every pair of receivers in the array although the correct solution for the array attitude may be determined from a subset of such potential solution sets. Another embodiment determines another set of potential solutions for another baseline vector when the baseline vectors of every pair of compared potential solutions fails to satisfy the predetermined criteria.
In one embodiment, selecting one of the pairs of potential solutions includes determining if a degree of geometric consistency between the corresponding pair of baseline vectors satisfies the predetermined criteria. In another embodiment, a value is assigned to each of the potential solutions in the first and second sets of potential solutions, the assigned value corresponding to a closeness of that potential solution to being a correct solution for the corresponding baseline vector. In this embodiment, selecting one of the pairs of compared potential solutions includes determining that the assigned values for the potential solutions in the selected pair of potential solutions satisfies the predetermined criteria.
A value is assigned to each compared pair of potential solutions. The value corresponds to a closeness of the compared pair to being a geometrically consistent solution for the attitude of the array. In one embodiment, the selected pair of potential solutions is determined to be the correct solution for the array attitude if the selected pair of potential solutions is the only pair of potential solutions that satisfies the predetermined criteria. In another embodiment, a highest assigned value and a next highest assigned value is determined for the compared pairs of potential solutions. The compared pair of potential solutions with the highest assigned value is selected as the correct solution for the attitude of the array if the highest assigned value exceeds the next highest assigned value by a predetermined margin.
At least one test can be performed on each potential solution for a baseline vector. A value is assigned to each potential solution for each baseline vector based on the result of each test. The values assigned to each potential solution in a pair of compared potential solutions are combined with the value assigned to the geometric consistency of that pair of potential solutions. This combination of values produces an overall value that is used when selecting a correct solution for the attitude of the array.
Potential solutions of some baseline vectors can also be eliminated as bad solutions based on the potential solutions for other baseline vectors. In one embodiment, the potential solution for the first baseline vector is eliminated as incorrect based on a geometric inconsistency of the first baseline vector with potential solutions of the second baseline vector in conjunction with other information.
In another aspect, the invention features a method for determining an attitude of the array which selects a set of receiver antenna locations in the array where the vectors joining the antenna locations together form a closed loop. A set of potential solutions is determined for each baseline vector defined by the selected set of antennas. One of the potential solutions from each of the sets of potential solutions is selected as a correct solution for the attitude of the array if the baseline vectors corresponding to the selected potential solutions together are geometrically consistent. In one embodiment, the baseline vectors of the selected potential solutions are determined to be geometrically consistent to the extent that such baseline vectors form a closed loop.
In another aspect, the invention features a positioning system for determining an attitude of an array of signal receivers that simultaneously receive signals emitted from a plurality of signal transmitters (e.g. GPS satellites). Each pair of receivers in the array defines a baseline vector. A processor determines from the received signals a first set of potential solutions for a first baseline vector defined by any pair of receivers in the array and a second set of potential solutions for a second baseline vector for any other pair of receivers in the array. A comparator compares each potential solution in the first set with each potential solution in the second set to determine a degree of geometric consistency between each pair of compared solutions. A selector selects one of the pairs of compared potential solutions as representative of the attitude of the array if the degree of consistency of that pair satisfies predetermined criteria.